The JK is perpendicular bisector of NL. So NJ = LJ.
Consider the triangle NJK and triangle LJK.
[tex]NJ=LJ\text{ (JK is perpendicular bisector of NL)}[/tex][tex]\angle NJK=\angle LJK\text{ (Each angle is 90 degree)}[/tex][tex]JK=JK\text{ (Common side)}[/tex]
So triangle NJK is congruent to triangle LJK. So segment lengths that are equal,
[tex]NK=LK[/tex][tex]NJ=LJ[/tex]
2.
The equation for x,
[tex]6x-5=4x+1[/tex]
Solve the equations for x.
[tex]\begin{gathered} 6x-4x=1+5 \\ 2x=6 \\ x=3 \end{gathered}[/tex]
So the length of side NK is,
[tex]\begin{gathered} NK=6\cdot3-5 \\ =18-5 \\ =13 \end{gathered}[/tex]
So the length of side NK is 13.
